Asteroids, comets, cosmic-dust granules, spacecrafts, as well as whatever
other freely spinning body dissipate energy when they rotate about
any axis different from a principal one. We show that the internal
dissipation takes place not so much at the frequency of body's precession
but rather at the second and higher harmonics. In other words, this simple
mechanical system provides an exellent example of an extreme non-linerity.
Moreover, it turns out that in some situations the inelastic dissipation
takes place at frequencies LOWER than the precession frequency (we call
this "exotic nonlinearity").

Earlier estimates by our predecessors ignored the non-linearity as well as
some other relevant subtleities. These oversights resulted in four to six
order underestimating the efficiency of the precession-relaxation process.
The new, more rigorous, treatment has been applied to the research of
cosmic-dust alignment and to the analysis of asteroidal and cometary
wobble. These results may find another application in the work on damping
of rotating spacecrafts.

Regarding the asteroidal and cometary wobble, estimates show that the
presently available angular resolution of spacecraft-based instruments
makes it possible to observe relaxation of cometary precession within a
year-long or, probably, even a several-month-long span of time. In case of
asteroids, the typical times are very sensitive to their inner structure
(rubble pile or solid chunk).

One of the applications of this research is the following: if one day we
manage to get statistics of the excited rotators in the mainbelt, then our
knowledge of the relaxation effectivenes will enable us to estimate the
frequency of collisions, data most relevant for our civilisation safety.

The other, more immediate application is this: from our knowledge of the
precession-damping rate of comets, we will be able to make conclusions on
their mechanical properties and inner structure.